Problem: Solve for $x$ : $x^2 - 10x + 24 = 0$
The coefficient on the $x$ term is $-10$ and the constant term is $24$ , so we need to find two numbers that add up to $-10$ and multiply to $24$ The two numbers $-6$ and $-4$ satisfy both conditions: $ {-6} + {-4} = {-10} $ $ {-6} \times {-4} = {24} $ $(x {-6}) (x {-4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -6) (x -4) = 0$ $x - 6 = 0$ or $x - 4 = 0$ Thus, $x = 6$ and $x = 4$ are the solutions.